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Keywords:
hypergeometric series; Bailey's cubic transformation; contiguous relation; reversal series; binomial coefficient
hypergeometric series; Bailey's cubic transformation; contiguous relation; reversal series; binomial coefficient
Summary:
By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the $_3F_2(x)$-series, we examine a class of $_3F_2(4)$-series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.
References:
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